(2n-5)(3n+1)=0

Solution for (2n-5)(3n+1)=0 equation:

Simplifying
(2n + -5)(3n + 1) = 0

Reorder the terms:
(-5 + 2n)(3n + 1) = 0

Reorder the terms:
(-5 + 2n)(1 + 3n) = 0

Multiply (-5 + 2n) * (1 + 3n)
(-5(1 + 3n) + 2n * (1 + 3n)) = 0
((1 * -5 + 3n * -5) + 2n * (1 + 3n)) = 0
((-5 + -15n) + 2n * (1 + 3n)) = 0
(-5 + -15n + (1 * 2n + 3n * 2n)) = 0
(-5 + -15n + (2n + 6n2)) = 0

Combine like terms: -15n + 2n = -13n
(-5 + -13n + 6n2) = 0

Solving
-5 + -13n + 6n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -3n)(5 + -2n) = 0

Subproblem 1
Set the factor '(-1 + -3n)' equal to zero and attempt to solve:

Simplifying
-1 + -3n = 0

Solving
-1 + -3n = 0

Move all terms containing n to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -3n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3n = 0 + 1
-3n = 0 + 1

Combine like terms: 0 + 1 = 1
-3n = 1

Divide each side by '-3'.
n = -0.3333333333

Simplifying
n = -0.3333333333
Subproblem 2
Set the factor '(5 + -2n)' equal to zero and attempt to solve:

Simplifying
5 + -2n = 0

Solving
5 + -2n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -2n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2n = 0 + -5
-2n = 0 + -5

Combine like terms: 0 + -5 = -5
-2n = -5

Divide each side by '-2'.
n = 2.5

Simplifying
n = 2.5
Solution
n = {-0.3333333333, 2.5}